Quotient of products

Average Error: 11.6 → 3.1

Time: 3.9s

Precision: binary64

Cost: 2512

\[ \begin{array}{c}[a1, a2] = \mathsf{sort}([a1, a2])\\ [b1, b2] = \mathsf{sort}([b1, b2])\\ \end{array} \]

Math

\[\frac{a1 \cdot a2}{b1 \cdot b2} \]

↓

\[\begin{array}{l} t_0 := \frac{a1 \cdot a2}{b1 \cdot b2}\\ t_1 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-324}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

FPCore

(FPCore (a1 a2 b1 b2) :precision binary64 (/ (* a1 a2) (* b1 b2)))

↓

(FPCore (a1 a2 b1 b2)
 :precision binary64
 (let* ((t_0 (/ (* a1 a2) (* b1 b2))) (t_1 (* (/ a2 b1) (/ a1 b2))))
   (if (<= t_0 (- INFINITY))
     t_1
     (if (<= t_0 -5e-324)
       t_0
       (if (<= t_0 5e-259)
         t_1
         (if (<= t_0 2e+302) t_0 (/ a2 (* b2 (/ b1 a1)))))))))

C

double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

↓

double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_0 <= -5e-324) {
		tmp = t_0;
	} else if (t_0 <= 5e-259) {
		tmp = t_1;
	} else if (t_0 <= 2e+302) {
		tmp = t_0;
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Java

public static double code(double a1, double a2, double b1, double b2) {
	return (a1 * a2) / (b1 * b2);
}

↓

public static double code(double a1, double a2, double b1, double b2) {
	double t_0 = (a1 * a2) / (b1 * b2);
	double t_1 = (a2 / b1) * (a1 / b2);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_0 <= -5e-324) {
		tmp = t_0;
	} else if (t_0 <= 5e-259) {
		tmp = t_1;
	} else if (t_0 <= 2e+302) {
		tmp = t_0;
	} else {
		tmp = a2 / (b2 * (b1 / a1));
	}
	return tmp;
}

Python

def code(a1, a2, b1, b2):
	return (a1 * a2) / (b1 * b2)

↓

def code(a1, a2, b1, b2):
	t_0 = (a1 * a2) / (b1 * b2)
	t_1 = (a2 / b1) * (a1 / b2)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1
	elif t_0 <= -5e-324:
		tmp = t_0
	elif t_0 <= 5e-259:
		tmp = t_1
	elif t_0 <= 2e+302:
		tmp = t_0
	else:
		tmp = a2 / (b2 * (b1 / a1))
	return tmp

Julia

function code(a1, a2, b1, b2)
	return Float64(Float64(a1 * a2) / Float64(b1 * b2))
end

↓

function code(a1, a2, b1, b2)
	t_0 = Float64(Float64(a1 * a2) / Float64(b1 * b2))
	t_1 = Float64(Float64(a2 / b1) * Float64(a1 / b2))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_0 <= -5e-324)
		tmp = t_0;
	elseif (t_0 <= 5e-259)
		tmp = t_1;
	elseif (t_0 <= 2e+302)
		tmp = t_0;
	else
		tmp = Float64(a2 / Float64(b2 * Float64(b1 / a1)));
	end
	return tmp
end

MATLAB

function tmp = code(a1, a2, b1, b2)
	tmp = (a1 * a2) / (b1 * b2);
end

↓

function tmp_2 = code(a1, a2, b1, b2)
	t_0 = (a1 * a2) / (b1 * b2);
	t_1 = (a2 / b1) * (a1 / b2);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1;
	elseif (t_0 <= -5e-324)
		tmp = t_0;
	elseif (t_0 <= 5e-259)
		tmp = t_1;
	elseif (t_0 <= 2e+302)
		tmp = t_0;
	else
		tmp = a2 / (b2 * (b1 / a1));
	end
	tmp_2 = tmp;
end

Wolfram

code[a1_, a2_, b1_, b2_] := N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]

↓

code[a1_, a2_, b1_, b2_] := Block[{t$95$0 = N[(N[(a1 * a2), $MachinePrecision] / N[(b1 * b2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(a2 / b1), $MachinePrecision] * N[(a1 / b2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], t$95$1, If[LessEqual[t$95$0, -5e-324], t$95$0, If[LessEqual[t$95$0, 5e-259], t$95$1, If[LessEqual[t$95$0, 2e+302], t$95$0, N[(a2 / N[(b2 * N[(b1 / a1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	11.6
Target	11.7
Herbie	3.1

\[\frac{a1}{b1} \cdot \frac{a2}{b2} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -inf.0 or -4.94066e-324 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 4.99999999999999977e-259

   1. Initial program 18.3

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]

   2. Applied egg-rr 4.4

      \[\leadsto \color{blue}{\frac{a2}{b1} \cdot \frac{a1}{b2}} \]

   if -inf.0 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < -4.94066e-324 or 4.99999999999999977e-259 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2)) < 2.0000000000000002e302

   1. Initial program 0.8

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]

   if 2.0000000000000002e302 < (/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

   1. Initial program 62.4

      \[\frac{a1 \cdot a2}{b1 \cdot b2} \]

   2. Applied egg-rr 7.5

      \[\leadsto \color{blue}{\frac{a2}{b2} \cdot \frac{a1}{b1}} \]

   3. Applied egg-rr 14.1

      \[\leadsto \color{blue}{\frac{a2}{\frac{b1}{a1} \cdot b2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -\infty:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq -5 \cdot 10^{-324}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 5 \cdot 10^{-259}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;\frac{a1 \cdot a2}{b1 \cdot b2} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{a1 \cdot a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.0
Cost	2268

\[\begin{array}{l} t_0 := \frac{\frac{a1 \cdot a2}{b1}}{b2}\\ t_1 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_2 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 4 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a1 \cdot a2 \leq 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 2
Error	6.0
Cost	2268

\[\begin{array}{l} t_0 := \frac{\frac{a1 \cdot a2}{b1}}{b2}\\ t_1 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_2 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 4 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a1 \cdot a2 \leq 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{+184}:\\ \;\;\;\;a1 \cdot \frac{a2}{b1 \cdot b2}\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \end{array} \]

Alternative 3
Error	7.8
Cost	1748

\[\begin{array}{l} t_0 := a2 \cdot \frac{a1}{b1 \cdot b2}\\ t_1 := \frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a1}{\frac{b1}{\frac{a2}{b2}}}\\ \end{array} \]

Alternative 4
Error	5.7
Cost	1488

\[\begin{array}{l} t_0 := \frac{\frac{a1 \cdot a2}{b1}}{b2}\\ t_1 := \frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	5.8
Cost	1488

\[\begin{array}{l} t_0 := \frac{\frac{a1 \cdot a2}{b1}}{b2}\\ t_1 := \frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a1 \cdot a2 \leq 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	5.8
Cost	1488

\[\begin{array}{l} t_0 := \frac{\frac{a1 \cdot a2}{b1}}{b2}\\ \mathbf{if}\;a1 \cdot a2 \leq -5 \cdot 10^{+225}:\\ \;\;\;\;\frac{a2}{b1} \cdot \frac{a1}{b2}\\ \mathbf{elif}\;a1 \cdot a2 \leq -1 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a1 \cdot a2 \leq 5 \cdot 10^{-277}:\\ \;\;\;\;\frac{a2}{b2 \cdot \frac{b1}{a1}}\\ \mathbf{elif}\;a1 \cdot a2 \leq 10^{+131}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{a2}{b2} \cdot \frac{a1}{b1}\\ \end{array} \]

Alternative 7
Error	11.5
Cost	448

\[\frac{a2}{b2 \cdot \frac{b1}{a1}} \]

Reproduce

herbie shell --seed 2022302 
(FPCore (a1 a2 b1 b2)
  :name "Quotient of products"
  :precision binary64

  :herbie-target
  (* (/ a1 b1) (/ a2 b2))

  (/ (* a1 a2) (* b1 b2)))